Efficient algorithms for reconstructing gene content by co-evolution

<p>Abstract</p> <p>Background</p> <p>In a previous study we demonstrated that co-evolutionary information can be utilized for improving the accuracy of ancestral gene content reconstruction. To this end, we defined a new computational problem, the Ancestral Co-Evolutionary (ACE) problem, and developed algorithms for solving it.</p> <p>Results</p> <p>In the current paper we generalize our previous study in various ways. First, we describe new efficient computational approaches for solving the ACE problem. The new approaches are based on reductions to classical methods such as linear programming relaxation, quadratic programming, and min-cut. Second, we report new computational hardness results related to the ACE, including practical cases where it can be solved in polynomial time.</p> <p>Third, we generalize the ACE problem and demonstrate how our approach can be used for inferring parts of the genomes of <it>non-ancestral</it> organisms. To this end, we describe a heuristic for finding the portion of the genome ('dominant set’) that can be used to reconstruct the rest of the genome with the lowest error rate. This heuristic utilizes both evolutionary information and co-evolutionary information.</p> <p>We implemented these algorithms on a large input of the ACE problem (95 unicellular organisms, 4,873 protein families, and 10, 576 of co-evolutionary relations), demonstrating that some of these algorithms can outperform the algorithm used in our previous study. In addition, we show that based on our approach a ’dominant set’ cab be used reconstruct a major fraction of a genome (up to 79%) with relatively low error-rate (<it>e.g.</it> 0.11). We find that the ’dominant set’ tends to include metabolic and regulatory genes, with high evolutionary rate, and low protein abundance and number of protein-protein interactions.</p> <p>Conclusions</p> <p>The <it>ACE</it> problem can be efficiently extended for inferring the genomes of organisms that exist today. In addition, it may be solved in polynomial time in many practical cases. Metabolic and regulatory genes were found to be the most important groups of genes necessary for reconstructing gene content of an organism based on other related genomes.</p

Minimal cost reconfiguration of data placement in a storage area network

Video-on-Demand (VoD) services require frequent updates in file configuration on the storage subsystem, so as to keep up with the frequent changes in movie popularity. This defines a natural reconfiguration problem in which the goal is to minimize the cost of moving from one file configuration to another. The cost is incurred by file replications performed throughout the transition. The problem shows up also in production planning, preemptive scheduling with set-up costs, and dynamic placement of Web applications. We show that the reconfiguration problem is NP-hard already on very restricted instances. We then develop algorithms which achieve the optimal cost by using servers whose load capacities are increased by O(1), in particular, by factor 1 + δ for any small 0 &lt; δ &lt; 1 when the number of servers is fixed, and by factor of 2 + ε for arbitrary number of servers, for some ε ∈ [0, 1). To the best of our knowledge, this particular variant of the data migration problem is studied here for the first time

Fairness-Free Periodic Scheduling with Vacations

Abstract. We consider a problem of repeatedly scheduling n jobs on m parallel machines. Each job is associated with a profit, gained each time the job is completed, and the goal is to maximize the average profit per time unit. Once the processing of a job is completed, it goes on vacation and returns to the system, ready to be processed again, only after its vacation is over. This problem has many applications, in production planning, machine maintenance, media-on-demand and databases query processing, among others. We show that the problem is NP-hard already for jobs with unit processing times and unit profits, and develop approximation algorithms, as well as optimal algorithms for certain subclasses of instances. In particular, we show that a preemptive greedy algorithm achieves a ratio of 2 to the optimal for instances with arbitrary processing times and arbitrary profits. For the special case of unit processing times, we present a 1.67-approximation algorithm for instances with arbitrary profits, and a 1.39-approximation algorithm for instances where all jobs have the same (unit) profits. For the last case, we also show that when the load generated by an instance is sufficiently large (in terms of n and m), any algorithm that uses no intended idle times yields an optimal schedule.

Tight bounds for online class-constrained packing

Currently on a leave in Bell Laboratorie